Can anyone tell me why my hands go numb while riding? I ride a mountain bike and I use bar ends so I can change hand position sometimes, but, after about a half an hour of riding my hands almost always go numb. Any suggestions?

This is sort of off topic, but my muscles in my arms tend to get tired easily and start to ache. Would pushups be of any help to train those muscles?

Yes. Pushups would help. Which part of your arms tire? Forearms? Triceps?

If your forearms are tiring make an effort not to squeeze the bar so hard. If it's your triceps try doing push-ups with your elbows tucked in your sides. That will target your tris more directly than a wider or normal position push up. Or look up triceps dips on google if you want to throw some variety in there.

Can anyone tell me why my hands go numb while riding? I ride a mountain bike and I use bar ends so I can change hand position sometimes, but, after about a half an hour of riding my hands almost always go numb. Any suggestions?

You are likely supporting too much of your weight on your arms. You should be putting your weight on your saddle. Have a fried hold your bike up from the rear while you sit on it with the cranks at 9 and 3 oclock. (feet on pedals) Put an index finger on each brake lever to support your front. Do not use anything but your index fingers.

Now quickly take them off the brakes (so they are touching nothing). Does your body want to fall forward drastically? If so, try nosing your saddle up. I have found that by having the nose of my saddle a tick higher than the rear i know longer have arm/shoulder trouble.

Also focus on your arms while you ride. Are you gripping the bar tightly? Are your arms tense. RELAX! Keep reminding yourself to relax your arms, there is no reason to be all tensed up in your arms.

It could also be that you're pinching a nerve in your wrist/heel of your hand. I've got Carpal tunnel problems, and numb hands is a constant aggravation. sucks
like has been said, try raising the handlebars a bit and make sure you've got as little weight as possible on your hands while riding.